Power networks with switches are hybrid systems--they have a finite set of governing equations that depend on time and possibly the state of the network.  Designing these discrete changes to either minimize or maximize some objective function is the purpose of hybrid optimal control.  For instance, one may wish to design time-dependent changes in transmission lines to stabilize a multimachine power network that would otherwise go unstable.  Solving the associated optimal control problem is challenging due to the integer constraints on the inputs found in the governing equations.  In this talk I will discuss a method that does not require a priori discretization and does not relax the optimization, but does provide guarantees on both convergence and computational complexity.  Moreover, at every iteration the algorithm returns a dynamically feasible solution.  The method parallels classical gradient descent methods from finite dimensions, but in an infinite-dimensional and nondifferentiable setting, making implementation of the algorithms reasonably straight forward.  I will illustrate the algorithmic technique on a power network example.